The Purpose of A Carbon tax
The purpose of a carbon tax is to internalise the externality. What this means is that the final price of the good should include the external cost and not just the private cost. It is similar to the ‘polluter pays principle.‘ This was incorporated into international law at the 1992 Rio Summit. It simply means those who cause environmental costs should be made to pay the full social cost of their actions.
In theory, the tax should equal the external cost. Therefore, the price consumers pay will be the social cost.
Demand will fall and the new equilibrium will be socially efficient because at this output, the marginal social cost equals the marginal social benefit.